Prove that if \[ \lim_{x\to a}\,f(x)=L\neq 0 \] and \[ \lim_{x\to a}\,g(x)=0 \] then the limit \[ \lim_{x\to a}\,\frac{f(x)}{g(x)} \] does not exist.
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Lesson Parent:
Problem:
Prove that if
\[
\lim_{x\to a}\,f(x)=L\neq 0
\]
and
\[
\lim_{x\to a}\,g(x)=0
\]
then the limit
\[
\lim_{x\to a}\,\frac{f(x)}{g(x)}
\]
does not exist.
Answer:
It is true that if \[ \lim_{x\to a}\,f(x)=L\neq 0 \] and \[ \lim_{x\to a}\,g(x)=0 \] then the limit \[ \lim_{x\to a}\,\frac{f(x)}{g(x)} \] does not exist.
